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- Herausgeber: Universidad del Valle
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Spanisch
Civil infrastructure systems are extraordinarily important for society. Our economy, security, health, and comfort depend directly or indirectly on the adequate transportation, habitat, and communication systems. Nowadays, in addition to the impact of strong natural and human made events, infrastructure's deterioration caused by natural use and aging is a concern of the engineering community around the world. As an example, the American Society of Civil Engineers (ASCE) have given an average grade of D to the infrastructure of the United States of America for more than 10 years with only a slight improvement in the 2001 report (American Society of Civil Engineers, 2009). Additionally, the last report states that 2.2 trillion dollars need to be invested in the next five years to achieve an acceptable level. The development and implementation of strategies to maintain, analyze, enhance, and optimize these civil infrastructure systems should be a priority. Strategies to maintain or improve existing structural systems usually require numerical models of the structure to analyze its behavior (Zárate & Caicedo, 2008). These numerical models are used to evaluate structural performance under specific conditions such as heavy loading (Schlune et al., 2009), earthquake motion (Alyami et al., 2009), wind loading (Kim et al. 2009) or human activity (Racic et al., 2009). Therefore, developing accurate models of existing structures is key to evaluate the vulnerability (Galati et al., 2008), detect damage (Teughels & De Roeck, 2004), study retrofit alternatives (Stehmeyer & Rizos, 2008) and predict the remaining useful life of structures (Fritzen & Kraemer, 2009). The accuracy of the numerical model refers to the ability to reproduce the response of the real structure having parameters with a realistic physical meaning. This implies the experimental characterization of the static and dynamic behavior of the structure to compare it with numerical results and tune the model.
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Marulanda Casas, Johannio
Modal identification using smart mobile sensing units / Johannio Marulanda Casas. -- Cali: Programa Editorial Universidad del Valle, 2014.
104 páginas ; 17 x 24 cm.-- (Libros de Investigación)
1. Ingeniería civil 2.Sensores móviles inteligentes I. Tít. II. Serie.
624cd 21 ed.
A1438272
CEP-Banco de la República-Biblioteca Luis Ángel Arango
Universidad del Valle
Programa Editorial
Título:Modal identification using smart mobile sensing units
Autor:Johannio Marulanda Casas
ISBN:978-958-765-114-0
ISBN-epub: 978-958-5164-25-3
Colección: Libros de Investigación
Primera edición
Rector de la Universidad del Valle: Iván Enrique Ramos Calderón
Vicerrectora de Investigaciones: Ángela María Franco Calderón
Director del Programa Editorial: Francisco Ramírez Potes
© Universidad del Valle
© Johannio Marulanda Casas
Diseño de carátula y diagramación: Hugo H. Ordóñez Nievas
Impreso en: Artes Gráficas del Valle S.A.S.
Universidad del Valle
Ciudad Universitaria, Meléndez
A.A. 025360
Cali, Colombia
Teléfono: (+57) (2) 321 2227. Telefax: (+57) (2) 330 88 77
Este libro, o parte de él, no puede ser reproducido por ningún medio sin autorización escrita de la Universidad del Valle.
El contenido de esta obra corresponde al derecho de expresión del autor y no compromete el pensamiento institucional de la Universidad del Valle, ni genera responsabilidad frente a terceros. El autor es el responsable del respeto a los derechos de autor y del material contenido en la publicación (fotografias, ilustraciones, tablas, etc.), razón por la cual la Universidad no puede asumir ninguna responsabilidad en caso de omisiones o errores.
Cali, Colombia, julio de 2014
Diseño epub:Hipertexto – Netizen Digital Solutions
CONTENT
CHAPTER 1
INTRODUCTION
Mode Shape Expansion
Mobile Sensing for Modal identification
Model Updating Cognitive System framework
Outline
CHAPTER 2
MIMS METHODOLOGY
State-of-the-art modal identification techniques
General Formulation of MIMS
Sinusoidal Excitation
Impulse Excitation
Ambient Vibration
Summary
CHAPTER 3
EXPERIMENTAL VALIDATION OF MIMS
Sinusoidal Excitation
Ambient Vibration
Summary
CHAPTER 4
THE FAST MODE IDENTIFICATION TECHNIQUE
Summary
REFERENCES
APENDIX A – DERIVATIONS
Derivation A.1
Derivation A.2
Derivation A.3
CHAPTER 1
INTRODUCTION
Civil infrastructure systems are extraordinarily important for society. Our economy, security, health, and comfort depend directly or indirectly on the adequate transportation, habitat, and communication systems. Nowadays, in addition to the impact of strong natural and human made events, infrastructure’s deterioration caused by natural use and aging is a concern of the engineering community around the world. As an example, the American Society of Civil Engineers (ASCE) have given an average grade of D to the infrastructure of the United States of America for more than 10 years with only a slight improvement in the 2001 report (American Society of Civil Engineers, 2009). Additionally, the last report states that 2.2 trillion dollars need to be invested in the next five years to achieve an acceptable level. The development and implementation of strategies to maintain, analyze, enhance, and optimize these civil infrastructure systems should be a priority.
Strategies to maintain or improve existing structural systems usually require numerical models of the structure to analyze its behavior (Zárate & Caicedo, 2008). These numerical models are used to evaluate structural performance under specific conditions such as heavy loading (Schlune et al., 2009), earthquake motion (Alyami et al., 2009), wind loading (Kim et al. 2009) or human activity (Racic et al., 2009). Therefore, developing accurate models of existing structures is key to evaluate the vulnerability (Galati et al., 2008), detect damage (Teughels & De Roeck, 2004), study retrofit alternatives (Stehmeyer & Rizos, 2008) and predict the remaining useful life of structures (Fritzen & Kraemer, 2009). The accuracy of the numerical model refers to the ability to reproduce the response of the real structure having parameters with a realistic physical meaning. This implies the experimental characterization of the static and dynamic behavior of the structure to compare it with numerical results and tune the model.
System identification and modal analysis methodologies are used to characterize the dynamic behavior of existing structures. These techniques use dynamic measurements to estimate modal parameters consisting of natural frequencies, damping ratios, modal participation ratios and mode shapes. Different types of dynamic tests can be performed on a system to characterize its behavior such as free vibration, impact, and resonance tests. However, these tests are not always convenient for civil infrastructure. Closing bridges and buildings is expensive and the equipment to perform these types of tests can be costly. The preferred approach for civil structures is the use of ambient vibration, generally caused by traffic, wind, and microtremors under normal operating conditions. In this case it is assumed that the excitation is a realization of a stochastic process (white noise) and stochastic system identification, output-only or operational modal analyses are used to characterize a structure dynamically (Peeters & Roeck, 2001).
Modal identification methodologies in civil engineering use a limited number of sensors placed at strategic points in the structure to identify its dynamic characteristics. The coordinates of the mode shapes are calculated at the sensor locations only, resulting in sparse identified mode shapes (Figure 1). However, applications such as model updating techniques require modal coordinates at degrees of freedom that have not been measured. The expansion of the identified coordinates or the reduction of the numerical model being updated are two approaches commonly used in the literature (Friswell & Mottershead, 1995). However, these methodologies often introduce errors in the model updating process.
Figure 1. Concept of sparse identified mode shapes.
An alternative to address the low spatial resolution is to install more sensors. In other words, use dense sensor networks. However, the cost of instrumentation and installation of dense sensor networks makes it a sometimes prohibited approach. Smart wireless sensors have been proposed for large instrumentation systems (Lynch, 2007; Spencer et al., 2004). The relative lower cost of the instruments and the easier installation of wireless sensors make them suitable to having a larger number of sensors. However, additional challenges on the network communication because of the large amount of data to be transmitted have to be addressed. In addition, algorithms should be computationally simple to reduce energy consumption on the battery powered sensors.
The main objective of this document is to formulate, evaluate, and validate an innovative modal identification methodology to estimate high spatial density mode shapes using mobile sensors. The methodology should require less number of sensors than traditional modal identification methods. Less data is also required. Specific goals are i) formulate the methodology for different excitation cases such as sinusoidal, impulse, and ambient vibration; ii) develop algorithms to implement the methodology; iii) evaluate the accuracy and sensitivity of the methodology to key parameters; iv) build a smart mobile sensing unit; and v) validate the proposed methodology using numerical and experimental tests.
MODE SHAPE EXPANSION
Mode shape expansion methods are used to calculate spatially dense mode shapes based on the information of discrete points, minimizing the impact of the low spatial resolution of measurements. These techniques can be classified into three main groups according to Levine-West et al. (1994): i) spatial interpolation techniques, which use a finite element model geometry to expand the mode shape; ii) properties interpolation techniques, which use the finite element model properties for the expansion; and iii) error minimization techniques, which intend to minimize the error between the expanded and the analytical mode shape using projection methods. Methods in the first group are sensitive to spatial discontinuities, quantity, and location of sensors and the mode pairing procedure. The Guyan method (Guyan, 1965), which assumes negligible inertial forces at the unmeasured DOF; and the Kidder method (Kidder, 1973), which uses the complete dynamic equations to calculate the modal coordinates at the unmeasured DOF, are included in the second group. The Procrustes method (Smith & Beattie, 1990), which uses an orthogonal projection, and the least-squares minimization methods are examples of the third group of modal expansion techniques.
Levine-West et al. (1994) studied the least-squares minimization with quadratic inequality constrains (LSQI), Procrustes, Guyan, and Kidder methods. Results indicated that the LSQI based on dynamic force equation have a better performance over the other methods, including the LSQI based on strain energy. The evaluation of the methods was performed with analytical and experimental data from the Micro-Precision interferometer (MPI) testbed, a lightly-damped truss-structure comprised of two booms and a vertical tower, located at the Jet Propulsion Laboratory in NASA.
Balmès (2000) proposes a bipartite classification of the expansion methods: i) subspace expansion methods, which select a subspace of possible displacements from a finite element model and perform a minimization of test errors to give a direct mapping between tested and expanded shapes; and ii) model-based minimization methods, which combine testing and modeling error measures for minimization. Modal/SEREP, static, dynamic, and hybrid methods, which find the subspace using only prior information, are included in the first group. The second group incorporates a more general class of methods, like the minimum dynamic residual expansion (MDRE) and the MDRE with test error (MDRE-WE) (Bobillot & Balmès, 2001). The evaluation of these methods’ performance is done using analytic and experimental data from the GARTEUR SM-AG-19 testbed (Balmès, 1997). Results indicate that MDRE-WE had the best performance in this particular application because of its test and modeling error trade-off. However, additional error sources for the MDRE-WE method, like model reduction, modeling errors, and measurements statistics, have to be considered.
In general, mode shape expansion methods can introduce errors into the modal identification process due to: i) discrepancy between the location of the sensors and the location of DOF in numerical models, and ii) modeling errors (Balmès, 2000; Pascual et al., 2005). Common solutions to address the discrepancy between the location of sensors and modeled DOF are ignoring distances between the sensor and the numerical DOF, modifying the FE model to match sensor locations, and adding nodes and rigid links in the FE model. In addition, analytical models are based on assumptions that may not correctly represent the structure. These assumptions generate modeling errors that need to be considered from a modal expansion perspective.
MOBILE SENSING FOR MODAL IDENTIFICATION
The use of mobile sensors for modal identification of civil structures has been practically unexplored. A similar concept has been applied with Laser Doppler Vibrometers (LDV) used in a continuously-scanning mode (Stanbridge & Ewins, 1999). A laser beam from the LDV is focused to a surface of interest and the velocity of the addressed point is measured using the Doppler shift between the incident and the reflected beam (Figure 2). Advantages of an LDV over other measurement devices are i) accessibility to difficult targets (e.g. too small or too hot); ii) no additional loading; iii) easy modification of the target point by the use of mirrors; and iv) high spatial density measurements. Some challenges for the use of the LDV are the influence of the speckle noise on the measured data (Martarelli & Ewins, 2006) and the limited size of the structure being measured.
Figure 2. Schematic of standard LDV.
From: http://en.wikipedia.org/wiki/User:Daguilar/CSLDV.
Stanbridge and Ewins (1999) describe several modal testing techniques using a Scanning Laser Doppler Vibrometer (SLDV). The vibration measurements along a line are obtained continuously passing the laser beam over the surface of a vibrating structure. The single signal collected from the LDV at a uniform or sinusoidal speed can be used for the identification of a polynomial that describes the operational mode shape of a structure. Successful applications in the modal identification of a cantilever steel plate and the measurement of rotating discs vibration are explored in the paper. The methodology was verified by comparing the results of the Continuous-Scan Laser Doppler Vibrometer (CSLDV) to those of traditional impact tests (Stanbridge et al., 2000). Improved results for two dimensional CSLDV were obtained with a sinusoidal area scan approach by Stanbridge et al. (2004).
Stanbridge et al. (2002) proposed a technique to use a CSLDV to derive the curvature equations of a beam or a plate and calculate the stress and strain distributions. A correction of the higher order polynomial coefficients of the identified operational mode shape was used, limiting the application to elements following the Euler beam theory without external forces applied at the scanned segment. The latest extension of the CSLDV methodology is the use of random excitation to excite a cantilever beam and identify the operational deflection shapes (Di Maio et al., 2010), maintaining the polynomial shape assumption.
Modal identification methodologies using CSLDV have been successful for uniform beam and plate elements. Challenges of the application of these methodologies to civil structures are i) the usable distance of the lasers is too small for most civil applications, ii) line of sight is needed, iii) CSLDV systems are relatively expensive, iv) the surface of civil structures is exposed to environmental factors, affecting its reflective properties.
This research proposes the use of a mobile sensor for modal identification in civil infrastructure. A fine grid of discrete points representing the operational mode shape is constructed using information of the vibration of the structure, avoiding the need for modal expansion, similar to the results of CSLDV. Furthermore, the methodology only requires the use of one or few single sensors to calculate high spatially dense mode shapes without any assumption about the shape (e.g. polynomial).
